Method for Measuring the Variance in a Measurement Signal, Method for Data Fusion, Computer Program, Machine-Readable Storage Medium, and Device

ABSTRACT

The disclosure relates to a method for measuring the variance in a measurement signal, comprising the following steps: filtering the measurement signal by means of a high-pass filter in order to obtain a filtered measurement signal; determining the variance by using the filtered measurement signal.

The present invention relates to a method for measuring a variance in ameasurement signal and to a method for data fusion. The presentinvention also relates to a computer program, a machine-readable storagemedium and a corresponding device, in particular for use insatellite-based navigation.

Prior art

U.S. Pat. No. 7,209,938 B2 discloses a filter technique using a Kalmanfilter, which uses an adaptive estimator for the measurement variance.The technique of the Kalman filter comprises a mechanism for signalfiltering. The mechanism for signal filtering further comprises a Kalmanfilter and a variance estimator.

In the technique of data fusion, in particular in navigation usinginertial sensors and GNSS, Kalman filters are often used. In addition toa model and measurement variables, these statistical filters requireinformation about the quality of the measurement data in the form of thevariance of the measurement data.

For measurement signals whose variance is not known or is variable,adaptive Kalman filters can be used, which modify the variances. To thisend, the states of the Kalman filter are usually also used and thevariances are estimated by complex matrix operations.

DISCLOSURE OF THE INVENTION

Against this background, with the present invention a method forestimating the noise parameters is proposed, in particular the variance,in accordance with the main claim.

The method is particularly suited for the measurement signals of aKalman filter for data fusion during the delay time, in order to achievea better and adaptive filter performance of the overall system.

It allows a resource-saving implementation, which is independent of themodel that underlies the Kalman filter.

Thus, the invention has more the character of a measurement than thecharacter of an estimate.

The core of the invention is the determination of the noise, inparticular of the variance, in the measurement signals of the Kalmanfilter exclusively on the basis of the measurement signals themselves.Thus the determination of the noise should be considered more like ameasurement of the noise. This is advantageous compared to theconventional systems, in which the noise is estimated and dependent onthe stored model.

With regard to the present invention, it should be emphasized that themeasurement of the variance takes place outside of the Kalman filter andtherefore does not depend on the inherent inertia within the Kalmanfilter. As a result, a rapid adaptation to changes in the measurementsignal is possible. Also advantageous is the fact that constant inputsignals more quickly give rise to a constant output signal. It isproposed to determine the variance of a measurement signal by the DCcomponent, and therefore the real signal, being suppressed using ahigh-pass filter, in particular a digital high pass filter.

The advantages of the invention are particularly noticeable when themethod is used in vehicles, e.g. for position determination based onsatellite-assisted navigation systems.

The invention is also associated with lower hardware resource costs.

The method comprises the steps:

filtering of the measurement signal using a high pass filter, in orderto obtain a filtered measurement signal;

determination of the variance on the basis of the filtered measurementsignal.

The measurement signal in the present case can be any type ofmeasurement signal. However, the invention originates from the findingthat particularly good results in terms of the data fusion of signals ofa satellite-based navigation device (GLASS signals) can be achieved withsignals of an inertial sensor, for example, an acceleration sensor.

According to an advantageous embodiment the high-pass filter is a linearphase filter.

Due to the use of a linear phase filter, all noise components have thesame group delay time.

Very simply, this can be achieved by the use of a finite impulseresponse (FIR) filter.

It has been shown that when a FIR filter is used the results of thevariance measurement are significantly improved if the coefficients ofthe high-pass filter are dependent on the sampling rate with which themeasurement signal is acquired.

Crucial to this method is to keep the group delay in the filter path aslow as possible, because the noise of the measurement signals can bedifferent depending on the driving situation.

Therefore, in a preferred embodiment of the method, the group delay ofthe high-pass filter is adapted to the delay in the variance relevant tothe measurement task.

A small group delay prevents a change in the noise from also beingrapidly carried over into a new variance, and therefore in the event ofrapid changes between driving conditions the calculation of the varianceis nevertheless correct.

In the specific application, i.e., the data fusion of GNSS signals withsignals of an inertial sensor, for example, an acceleration sensor, agroup delay of between 50 ms and 100 ms has proven advantageous. Therecommended value for the group delay is 80 ms.

According to an efficient implementation of the present method, afterthe filtering step a second filtering step is carried out, wherein inthe second filtering step the variance determined from the previouslyfiltered measurement signal is filtered using a low-pass filter.

According to a simple embodiment, using a low-pass filter, in particulara PT1 low-pass filter, the mean value of the sum of squares can beformed continuously. This simplification is based on the recognitionthat the mean value of the sum of squares corresponds directly to thevariance, if the mean value through the previous high pass filter isassumed to be 0.

The cutoff frequencies of the filter used are chosen according to thefrequency at which the signal still contains information relevant to themeasurement task.

Therefore, in accordance with one embodiment of the method the cutofffrequencies of the high-pass filter or low-pass filter are based on thefrequency at which the signal still contains information relevant to themeasurement task.

In the area of driving dynamics of road vehicles, depending on thenumber of vehicle tracks this is approximately 3 Hz to 20 Hz, inparticular 5 Hz to 20 Hz.

According to one advantageous embodiment of the method, in thedetermination step, the variance is calculated using a runningcalculation, and/or using a running mean and/or using a running mean ofthe sum of squares.

This represents a simple implementation for calculating or measuring thevariance from the high-pass filtered input signal.

In order not to obtain the entire history of the measurement signalduring the continuous calculation using the running mean and the runningmean of the sum of squares, but to consider only the most recent periodof time instead, in accordance with an extended alternative design inthe determination step a third filtering step is carried out and in thisstep, the running average is filtered.

Thus in a simple way, the variance calculation or measurement can berestricted to the relevant measurement period being searched.

A further aspect of the present invention is a method for data fusionusing a Kalman filter, wherein a first input signal is a measurementsignal and a second input signal is a variance of the measurementsignal, and wherein the variance is measured using an embodiment of themethod according to the present invention.

Of particular advantage here is an embodiment of the method for datafusion, according to which the variance is measured outside of theKalman filter.

A further aspect of the present invention is a computer program, whichis designed to carry out all steps of the method for measuring avariance and/or the method for data fusion, and a machine-readablestorage medium on which an embodiment of this computer program isstored.

In addition, one aspect of the present invention is a device which isdesigned to carry out all steps of the method for measuring a varianceand/or the method for data fusion.

For the implementation of such a device as an embedded system, as usedfor example in vehicle sensors and vehicle control units, it isparticularly advisable to use divisors in the form of powers of two, inorder to replace the division operation by an arithmetic shiftoperation.

In the following, embodiments of the present invention are presented andexplained based on the drawings. Shown are:

FIG. 1 a block circuit diagram of an embodiment of the presentinvention;

FIG. 2 a graph with input signals 1 to 4;

FIG. 3a a graph with variance calculations based on input signal 1 withdifferent methods;

FIG. 3b a graph with variance calculations based on input signal 2 withdifferent methods;

FIG. 3c a graph with variance calculations based on input signal 3 withdifferent methods;

FIG. 3d a graph with variance calculations based on input signal 4 withdifferent methods;

FIG. 4 a block circuit diagram;

FIG. 5 a flow diagram of an embodiment of the method for measuring thevariance in a measurement signal according to the present invention;

FIG. 6 a flow diagram of an embodiment of a method for data fusionaccording to the present invention.

FIG. 1 shows a block circuit diagram of an embodiment of the presentinvention. The block diagram clearly shows the core of the presentinvention. Sensors S deliver sensor signals or measurement signals to apost-processing unit. For the data fusion of sensor signals it isadvantageous to use a Kalman filter K, which is applied to themeasurement signals. For this purpose, the measurement signals are fedon the one hand to the Kalman-filter K, and the measurement signals arealso fed to a filter, here a high-pass filter HP, to suppress the DCcomponent, hence the real signal. This filtered measurement signal isthen fed to the variance calculation or measurement in accordance withthe presented method 500. The measured variance is in turn fed to theKalman filter K and then evaluated as a further input variable to thedata fusion.

FIG. 2 shows a graph with four measurement signals (signal 1 to 4). Ascan be seen from the graph, the measurement signals differ in theiramounts of variance, in the following figures, in other graphs theresults of various methods for determining the variance are shown incomparison to an embodiment of the method of the present invention.

FIGS. 3a to 3d show graphs with results of the variance calculation inaccordance with the window method and a pure low-pass filtering, incomparison to an embodiment of the method 500 of the present invention.

The results clearly show the power of the invention described, since theresults of the embodiment of the method of the present invention vary ina much narrower range about the reference variable, which is designatedas the input variance.

It is therefore clear that the present invention is applicable to a verywide range of input signals and delivers good results.

FIG. 4 shows a block circuit diagram of an embodiment of a system havinga device according to the present invention.

FIG. 4 shows two sensors S1 and S2, the sensor signals of which, andhence their measurement signal, are fused by means of a Kalman filter K.

To achieve this, the sensors S1, S2 input their measurement signal, onthe one hand, directly into the Kalman-filter K as an input signal. Inaddition, the measurement signals are filtered in accordance with themethod 500 of the present invention by means of a high-pass filter HP.The measurement signal filtered in this way is then filtered using alow-pass filter TP. The result of this filter step is input as a(measured) variance of the respective measurement signal into the Kalmanfilter K as an additional input variable.

The combination of high-pass and low-pass filter is also referred to asa band-pass filter BP. Thus, as an alternative to two individual filtersa band-pass filter BP can also be used.

It goes without saying that the filters HP, TP, BP can be designed indifferent ways. The filters can be implemented in hardware or software,or as a combination thereof.

The resulting output of the Kalman filter K is the fused result of thetwo measurements or sensor signals.

In the field of driving dynamics of road vehicles the relevantinformation can be found in the signal between 3 Hz to 20 Hz, inparticular from 5 Hz to 20 Hz.

These boundary conditions can be used to derive the result for thehigh-pass filter HP that the cutoff frequency of the low-pass filter TP,from which the high-pass filter HP can be generated (e.g. by inversion),should lie between approximately 5 Hz and 10 Hz, because due to theminimum possible group delay the damping will not be very high, even upto 20 Hz. The low-pass filter TP should have a cutoff frequency of atleast 2 Hz, also in order not to contribute an. excessively high valueto the group delay.

For use in motor vehicles, a 16th order FIR high-pass filter with thecoefficients bhp=[1, 16, 36, 55, 73, 84, 93, 102, −920, 102, 93, 84, 73,55, 36, 16, 1] and ahp=1024 and an infinite impulse response (IIR)low-pass filter with the coefficients btp=[1] and atp=[16, −15] areproposed for a sampling rate of 200 Hz. This achieves a group delay inthe passband of approximately 8 to 15 samples. At a sampling rate of 200Hz this corresponds to a group delay of 40 ms to 75 ms.

FIG. 5 shows a flow diagram of an embodiment of a method for measuringthe variance in a measurement signal according to the present invention.

In step 501, the measurement signal is filtered using a high-pass filterin order to obtain a filtered signal.

In step 502, on the basis of the filtered measurement signal thevariance in the measurement signal is determined.

FIG. 6 shows a flow diagram of an embodiment of a method for data fusionin accordance with the present invention.

In step 601, input signals are fused by means of a Kalman filter,wherein for the determination of the variance of the input signals amethod for measuring the variance in a measurement signal according tothe present invention is applied.

1. A method for measuring a variance in a measurement signal, the methodcomprising: filtering the measurement signal using a high pass filter toobtain a filtered measurement signal; and determining the variance basedon the filtered measurement signal.
 2. The method as claimed in claim 1,wherein the high pass filter is a linear phase filter.
 3. The method asclaimed in claim 2, wherein coefficients of the high pass filter aredependent on a sampling rate with which the measurement signal isdetected.
 4. The method as claimed in claim 2, further comprising:adapting a group delay of the high pass filter to a delay in thevariance relevant to a measurement task.
 5. The method as claimed inclaim 1, further comprising: after the filtering of the measurementsignal, determining the variance by filtering the previously filteredmeasurement signal using a low pass filter.
 6. The method as claimed inclaim 5, wherein cutoff frequencies of at least one of the high passfilter and the low pass filter are based on a frequency at whichinformation relevant to a measurement task is still present in themeasurement signal.
 7. The method as claimed in claim 1, the determiningof the variance further comprising: calculating, the variance using atleast one of a running calculation a running mean, and a running mean ofa sum of squares.
 8. The method as claimed in claim 5, the determiningof the variance further comprising: filtering a running mean value.
 9. Amethod for data fusion using a Kalman filter, the method comprising:receiving a measurement signal as a first input signal and a variance ofthe measurement signal as a second input signal, wherein the variance ofthe measurement signal is measured by (i) filtering the measurementsignal using a high pass filter to obtain a filtered measurement signal,and (ii) determining the variance based on the filtered measurementsignal; and fusing the measurement signal with at least one third inputsignal using the Kalman filter.
 10. The method as claimed in claim 9,wherein the variance is measured outside of the Kalman filter.
 11. Themethod of claim 1, wherein the method is executed by a non-transitorycomputer program.
 12. The method of claim 11, wherein the non-transitorycomputer program is stored on a computer-readable storage medium.
 13. Adevice for measuring a variance in a measurement signal, the devicebeing configured to: filter the measurement signal using a high passfilter to obtain a filtered measurement signal; and determine thevariance based on the filtered measurement signal.
 14. The method asclaimed in claim 2, wherein the high pass filter is a Finite ImpulseResponse filter.
 15. The method as claimed in claim 4, the adaptingfurther comprising: adapting the group delay to be between 50 ms and 100ms.
 16. The method as claimed in claim 15, the adapting furthercomprising: adapting the group delay to be 80 ms.
 17. The method asclaimed in claim 6, wherein the cutoff frequencies are located between 2Hz and 20 Hz.
 18. The method as claimed in claim 17, wherein the cutofffrequencies are located at 5 Hz and 10 Hz.